Groups that do not act by automorphisms of codimension-one foliations

2000/08/01 by Renato Feres, Feres, Renato, Dave Witte +1
Mathematics · #22F50 (Secondary) #57R30 (Primary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:22F50 #msc:57R30

paper · pdf · doi:10.48550/arxiv.math/0008012

Latex2e file, 15 pages, no figures

arxiv created 2000/08/01 · openalex publication_date 2000/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of E.Ghys, lattices in simple Lie groups of real rank at least two have this property.) Suppose that such a G acts on a compact manifold M by automorphisms of a codimension-one C2 foliation, F. We show that if F has a compact leaf, then some finite-index subgroup of G fixes a compact leaf of F. Furthermore, we give sufficient conditions for some finite-index subgroup of G to fix each leaf of F.

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